Jimmy Akin has argued for some time, quite plausibly, that the most authoritative censures of contraception by the Catholic Church are explicitly directed toward Christian married couples, and that the misconception that it is broader than this is due in part to bad information and in part to bad translation. He discusses one part of that argument here. There is in fact good reason to think that some of the reasons for rejecting the use of contraception in Christian marriage would also support the conclusion that at least much use of contraception outside of it would be rejected as well; but the extent of this has never been officially pronounced, and, indeed, has barely even been discussed.
As I've said before, Humanae Vitae is not on the subject of contraception but explicitly on the subject of how to have a marriage-friendly modern society, with contraception and other technological quesions being some of the major issues that come up as part of that problem. The conclusions about contraception there do not build on any simple argument, but on several complex strands: (1) the theology of marriage as a sacrament; (2) a single species-level point of natural law (which I've talked about here) along with natural-law precepts relevant to sex in a broader or more indirect way; (3) respect for the whole natural functioning of the human organism, which might be called the integrity of the rational animal; (4) a virtue-theoretical account of familial love, both between spouses and between parents and children, as part of human civilization; and (5) the function of marriage as a source of natural growth for the Church. It is not, in fact, difficult to find all of these points all over various pronouncements on the subject; but, except for very garbled versions of (2), one rarely finds any of it in summaries. It's very much a case of "What Everyone Knows" drowning out what is demonstrably the case. Catholics themselves have been major contributors to the confusion, including, unfortunately, Catholic priests of the kind who like to open their mouths before they use their minds (and reading skills!), although they are hardly the only ones to blame for it.
Actually, this sort of furor has been pretty common for quite some time now. The Church had almost exactly the same problems with the moral theology of truth-telling in the nineteenth century that it began to have with the moral theology of marital sex in the twentieth century; and while it surely says something about our society that the Victorian and Edwardian British were in this sort of furor over candour and we are in it over condoms, one still sees the same breakdowns of communication, the same kinds of deliberate misrepresentation in polemic, and the same steady attempt to oversimplify and drop all qualifications. And that was when the Church could build on Alphonsus Liguori, a far better expositor of natural law and virtue than any Catholics pontificating on the subject today. Modern moral theology is really in shambles; its expositors are in general simply not intellectually up to the task, and the relative few who are cannot do everything on their own. But even if they were, the problems would not go away; all the problems would arise because they result not from any particular content or failing but from the structure of Catholic controversy itself, and Catholic controversy we've had in one form or another for a very long time. (The Suburban Banshee gives a handful of other examples, for those who are interested.)